Master of Science Robin Schabert will Friday September 20th, 2024, at 12:15 hold his disputas for the PhD degree in Science. The title of his thesis is:
“Combinatorics and semi-algebraic geometry of orbit spaces”
Algebraic geometry studies the set of common zeros of a system of polynomials in one or several variables - most commonly over algebraically closed fields. Real algebraic geometry studies sets defined by a finite system of polynomial inequalities.
A starting point for modern real algebraic geometry can be traced back to Hilbert: In 1888, Hilbert showed the existence of nonnegative polynomials which are not sums of squares of polynomials. In 1900, he posed his famous 23 problems and, in particular, the 17th can be stated as follows: Is every nonnegative polynomial a sum of squares of rational functions?
Artin's solution to Hilbert’s 17th problem can be seen as a kick-off for real algebraic geometry. This thesis deals with real symmetric polynomials and the results are closely related to an answer of Hilbert's 17th problem for symmetric polynomials: A characterization of all symmetric nonnegative polynomials.
Professor Petter Brändén, KTH Royal Institute of Technology, Stockholm, Sweden. (1. opponent)
Assoc. Prof. Claudia Malvenuto, La Sapienza University, Rome, Italy (2. opponent)
Professor Trygve Johnsen, IMS, UiT, Tromsø (internal member and leader of the committee)
The disputas and trial lecture will be streamed from these sites:
Disputas (12:15 - 15:00)
Trial Lecture (10:15 - 11:00)
The thesis is available at Munin here.